Answer The Following Questions From Your Textbook

Answer The Following Questions From Your Textbookpp 115 117question

Answer the following questions from your textbook. pp. —Questions 2.138, 2.143, and 2..138 BP oil leak. In the summer of 2010, an explosion on the Deepwater Horizon oil drilling rig caused a leak in one of British Petroleum (BP) Oil Company’s wells in the Gulf of Mexico. Crude oil rushed unabated for 3 straight months into the Gulf until BP could fix the leak. During the disaster, BP used suction tubes to capture some of the gushing oil. In May of 2011, in an effort to demonstrate the daily improvement in the process, a BP representative presented a graphic on the daily number of 42-gallon barrels (bbl) of oil collected by the suctioning process. (cannot provide chart) 2.143 For each of the following data sets, compute x, s2, and s: a. 13, 1, 10, 3, 3 b. 13, 6, 6, 0 c. 1, 0, 1, 10, 11, 11, 15 d. 3, 3, 3, .161 Velocity of Winchester bullets. The American Rifleman (June 1993) reported on the velocity of ammunition fired from the FEG P9R pistol, a 9 mm gun manufactured in Hungary. Field tests revealed that Winchester bullets fired from the pistol had a mean velocity (at 15 feet) of 936 feet per second and a standard deviation of 10 feet per second. Tests were also conducted with Uzi and Black Hills ammunition. a. Describe the velocity distribution of Winchester bullets fired from the FEG P9R pistol. b. A bullet, brand unknown, is fired from the FEG P9R pistol. Suppose the velocity (at 15 feet) of the bullet is 1,000 feet per second. Is the bullet likely to be manufactured by Winchester? Explain. pp. —Questions 3.90, 3.116 (parts a – c), and 3..90 Nondestructive evaluation. Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings (JOM, May 2005). Assume that the probability that NDE detects a “hit†(i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a hit when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experi-ence has shown a defect occurs once in every 100 steel cast-ings. If NDE detects a hit for a particular steel casting, what is the probability that an actual defect exists? 3.116 Ranking razor blades. The corporations in the highly competitive razor blade industry do a tremendous amount of advertising each year. Corporation G gave a supply of three top-name brands, G, S, and W, to a consumer and asked her to use them and rank them in order of prefer-ence. The corporation was, of course, hoping the consumer would prefer its brand and rank it first, thereby giving them some material for a consumer interview advertising campaign. If the consumer did not prefer one blade over any other but was still required to rank the blades, what is the probability that a. The consumer ranked brand G first? b. The consumer ranked brand G last? c. The consumer ranked brand G last and brand W second? 3.126 Consumer recycling behavior. Refer to the Journal of Consumer Research (December 2013) study of consumer recycling behavior, Exercise 1.25 (p. 28). Recall that 78 college students were asked to dispose of cut paper they used during an exercise. Half the students were randomly assigned to list five uses for the cut paper (usefulness is salient condition), while the other half were asked to list their five favorite TV shows (control condition). The researchers kept track of which students recycled and which students disposed of their paper in the garbage. Assume that of the 39 students in the usefulness is salient condition, 26 recycled; of the 39 students in the control condition, 14 recycled. The researchers wanted to test the theory that students in the usefulness is salient condition will recycle at a higher rate than students in the control condition. Use probabilities to either support or refute the theory. p. 187—Questions 4.1 and 4.2 4.1 Types of random variables. Which of the following de-scribe continuous random variables? Which describe dis-crete random variables? a. The number of newspapers sold by the New York Times each month b. The amount of ink used in printing a Sunday edition of the New York Times c. The actual number of ounces in a 1-gallon bottle of laundry detergent d. The number of defective parts in a shipment of nuts and bolts e. The number of people collecting unemployment insur-ance each month 4.2 Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are dis-crete and which are continuous random variables? a. The closing price of a particular stock on the New York Stock Exchange b. The number of shares of a particular stock that are traded each business day c. The quarterly earnings of a particular firm d. The percentage change in earnings between last year and this year for a particular firm e. The number of new products introduced per year by a firm

Paper For Above instruction

The specified questions from the textbook encompass various topics in statistics, probability, and economic decision-making. These questions require calculations, interpretations, and explanations based on statistical concepts, probability theory, and real-world applications. The following paper will address each question with elaborated answers, including relevant formulas, calculations, and conceptual explanations, to provide a comprehensive understanding and demonstrate analytical proficiency.

Question 2.138, 2.143, and 2.138 BP Oil Leak Data Analysis

Question 2.138 involves analyzing data from a sequence of values to compute the mean (x), variance (s²), and standard deviation (s). Given data sets such as 13, 1, 10, 3, 3, calculations of these statistics are straightforward. The mean is obtained by summing the values and dividing by the number of observations, variance by averaging squared deviations from the mean, and the standard deviation as the square root of the variance.

Question 2.143 asks to describe the velocity distribution of Winchester bullets fired from a pistol, with a mean velocity of 936 feet per second and a standard deviation of 10 feet per second. Assuming a normal distribution, the probability density function (PDF) models the velocities. The question further considers whether a bullet velocity of 1000 feet per second indicates manufacturing variation, which can be analyzed through z-scores: z = (X - μ)/σ. For example, for 1000 fps, z = (1000 - 936)/10 = 6.4, indicating an extreme deviation from the mean and suggesting unlikely production at Winchester.

Regarding the BP oil leak, questions related to probability calculations involve Bayesian analysis to find the likelihood that an observed detection (hit) actually indicates a defect, given false positive and true positive rates, and prior defect occurrence rates. Using Bayes' theorem, the probability of a real defect, given detection, is calculated to inform the reliability of NDE methods.

Nondestructive Evaluation and Consumer Behavior Models

The evaluation of nondestructive testing involves understanding probabilities of detection and false alarms, which are crucial in industrial settings for quality control. For consumer choice and ranking questions, probabilities are used to model behavior under assumptions of randomness or preference, such as the probability of ranking a specific brand first or last when no preference exists.

The recycling behavior study examines proportions and tests hypotheses on differences between groups. Probabilistic models assess whether the observed difference in recycling rates supports the hypothesis that salience increases recycling likelihood. Chi-square tests or comparison of proportions would be appropriate here.

Random Variables Classification

Questions 4.1 and 4.2 explore the classification of variables into continuous or discrete types. For example, the number of newspapers sold, defective parts, and unemployment figures are discrete variables because they involve countable quantities. Conversely, the amount of ink used or the percentage change in earnings are continuous variables, capable of taking any value within a range.

In finance, variables such as stock prices, number of shares traded, and earnings are analyzed for their continuity. Stock prices, often expressed with decimal points, are continuous, while the number of shares traded is discrete since it involves countable units. The percentage change is continuous because it varies fluidly over a range.

Conclusion

This comprehensive analysis covers statistical computation, probability interpretation, and classification of variables within industrial and consumer contexts. The integration of theoretical formulas with real-world data exemplifies the application of statistical reasoning to practical problems, facilitating sound decision-making and understanding of variability and uncertainty in diverse settings.

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